Compact binary evolutions with the Z4c formulation

David Hilditch, Sebastiano Bernuzzi, Marcus Thierfelder, Zhoujian Cao, Wolfgang Tichy, and Bernd Brügmann
Phys. Rev. D 88, 084057 – Published 30 October 2013

Abstract

Numerical relativity simulations of compact binaries with the Z4c and Baumgarte-Shapiro-Shibata-Nakamura-Oohara-Kojima (BSSNOK) formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of nonvacuum spacetimes, the constraint violations due to truncation errors are between 1 and 3 orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions, we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of 4 smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the Arnowitt-Deser-Misner mass from surface integrals. For equal-mass nonspinning binary puncture black hole evolutions, we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of 2 smaller. In the same evolutions, we find that away from the punctures the Hamiltonian constraint violation is reduced by between 1 and 2 orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirms earlier results in spherical symmetry. The boundary conditions avoid spurious and nonconvergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge.

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  • Received 17 June 2013

DOI:https://doi.org/10.1103/PhysRevD.88.084057

© 2013 American Physical Society

Authors & Affiliations

David Hilditch1, Sebastiano Bernuzzi1, Marcus Thierfelder1, Zhoujian Cao2, Wolfgang Tichy3, and Bernd Brügmann1

  • 1Theoretical Physics Institute, University of Jena, 07743 Jena, Germany
  • 2Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 3Department of Physics, Florida Atlantic University, Boca Raton, Florida 33431, USA

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Issue

Vol. 88, Iss. 8 — 15 October 2013

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